Geometric Transformations and Tensor Product

This contribution describes new useful geometric transformations using the tensor product. The geometric transformations are used widely in many applications, especially in CAD/CAM systems, systems for Civil Engineering, computer graphics, virtual and augmented reality, etc. The basic geometric transformations, e.g. rotation, translation, scaling, etc., are usually applied on points represented in homogeneous coordinates and described in many relevant books. However, there are also other primitives, e.g. lines, planes, normal “vector” of a line, plane, triangle, etc., on which some geometric transformations can be applied.